Utility has a standard deviation of 40 percent and the return on the Commodity

# Utility has a standard deviation of 40 percent and

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Utility has a standard deviation of 40 percent, and the return on the Commodity has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. Emmy would like to plot the variance of the portfolio for each of three cases—covariance of 0.12, 0, and –0.12—in order to understand how the variance of such a portfolio would react. Do the calculation for all three cases (0.12, 0 and –0.12), assuming an equal proportion of each stock in the portfolio. LO 5 Solution: 12 2 1 2 2 2 2 2 1 2 1 2 2 ) ( σ σ σ x x x x R Var port asset + + = Case 1, σ 12 = 0.12: (0.5) 2 × (0.4) 2 + (0.5) 2 × (0.3) 2 + 2 × (0.5) × (0.5) × (0.12) = 0.1225 Case 2, ρ = 0.0: (0.5) 2 × (0.4) 2 + (0.5) 2 × (0.3) 2 + 2 × (0.5) × (0.5) × (0.0) = 0.0625 Case 3, σ 12 = -0.12: (0.5) 2 × (0.4) 2 + (0.5) 2 × (0.3) 2 + 2 × (0.5) × (0.5) × (-0.12) = 0.0025 